Angular Resolution
Resolution refers to the smallest angle that can be observed. In other word the ability to separate two closely spaced object into two individual things. You may think of this as clarity. Angular resolution is dependent upon the diameter of the observing instrument. When fully dark adapted the human eye has a pupil diameter of around 8 mm. Typical binoculars have lenses with a diameter of 50 mm. Telescopes have a large variety of diameter form 60 mm up to 10 meters.
The limiting angular resolution of the eye, a lens or telescope can be estimated using Dawes equation,
resolution in arc sec = 11.6/D, where D = diameter in cm of the objective lens.
However, more practical limits are:
- the human eye: can split binaries with separations of 700 or more arcsec,
- 7x50 binoculars: can split binaries with separations of 100 or more arcsec, and
- a 20 cm or 8 inch telescope: on an excellent night can split binaries with separations as small as 1 arcsec.
Because we must observe through the Earth's atmosphere, which is full of turbulence it is no really practical to expect to view binary stars closer together than 1 arc second. This turbulence causes the image produced by a telescope to become blurred and to dance around or twinkle. Astronomers refer to this as "seeing". When the seeing is really bad, like after the passage of a strong cold front your unaided eye can detect the bad seeing conditions because the stars twinkle a lot.
|
Diagram showing resolution of human eye. |
|
Diagram showing resolution of a small telescope. |
|
Diagram showing how turbulence affects image quality. |
Image of a wide binary star.
Some binary stars can be seen with the unaided eye.
With the aid of binoculars about one hundred or more binary stars can be seen.
Image of a binary that can be resolved with binoculars.
Image of a close telescopic binary.
With a small telescope of about 8 inch aperture thousands of binary stars can be observed. Include an image of a amateur telescope here.
A simple but important observation that can be made of binary stars is to follow the relative orbit of the stars around their common center-of-mass. In a binary system the brighter star is call the "primary' and the fainter stars the "secondary". It is simplest to make the position angle and separation measurements of the secondary relative to the primary, as if the seconday orbit the primary. The position angle (PA) is measured as shown in the diagram to the right. PA values assume that north is zero degrees and the angle is measured in a easterly direction. In most astronomical charts north is up and east is to the left. NOT all charts are done this way so you should always check for cardinal direction orientation. The position angle shown to the right is around 228 degrees. Angular separations are typically measured in arc seconds and is the angler distance between the two stars. Their actual separation in Astronomical Units, or kilometer cannot be determined unless the distance to the pair is known. Because visual binary stars have orbital periods which may be tens, hundreds or even thousands of years it may take several lifetimes to observe a complete orbital cycle. Professional astronomers do not have the time to keep up with these long period obits. Therefore, amateur astronomers can make a real contribution to the astronomical data base by make position angle and separation measurement on visual binary stars.
